1. Algebra: Equations and Inequalities
CHAPTER 6
Algebra: Equations and Inequalities

2. Linear Inequalities in One Variable
6.4
Linear Inequalities in One Variable

3. Objectives
Graph subsets of real numbers on a number line.
Solve linear inequalities.
Solve applied problems using linear inequalities.

4. Linear Inequalities
A linear inequality : ax + b ≤ c where the inequality symbol can be <, >, ≤, or ≥. Solving an inequality is the process of finding the set of numbers that make an inequality a true statement. A solution set is the set of all numbers that satisfy the inequality.

5. Example: Graphing Subsets of Real Numbers

6. Graphing Subsets of Real Numbers on a Number Line

7. Solving Linear Inequalities in One Variable
The procedure for solving linear inequalities is the same as the procedure for solving linear equations, with one important exception: When multiplying or dividing both sides of the inequality by a negative number, reverse the direction of the inequality symbol, changing the sense of the inequality.

8. Example: Solving a Linear Inequality
Solve and graph the solution set: 6x – 12 > 8x + 2
Solution: We will get x by itself on the left side.
The solution set is {x| x < 7}. The graph is:

9. Example: Solving a Three-Part Inequality
Solve the three part inequality:
Solution:
The solution set is { x| 2 < x ≤ 1}. The graph is: